Back in August Gary Hudson was a guest on the Space Show podcast discussing the recent NAIC grant the Space Studies Institute received involving SSI's Mach effect thruster propelled Proxima B probe. I asked whether Mach effect thrusters violated any conservation laws. He replied that although it might seem that way if one only looked at the thruster and probe by themselves, one has to take into account the energy and momentum of the entire universe. This is my first crack at that.

Suppose we have a coordinate system fixed to a Mach effect thruster. The thruster developes thrust by pushing against the universe so the thrust can be calculated (in Newtonian terms for simplicity, the result is identical in relativistic terms) as the time rate of change of the momentum of the universe:

F = d/dt(mu)

where

F - Mach effect thrustm - mass of universeu - velocity of universe

Since m is constant we have:

F = m du/dt (equation 1)

Mach effect power is the time rate of change of the kinetic energy of the universe:

P = d/dt( m u^2 / 2)

where

P - Mach effect power

Again, m is constant so this becomes:

P = m u du/dt (equation 2)

Substituting equation 1 into equation 2 gives:

P = F u (equation 3)

Equation 3 implies that Mach effect thruster performance is heavily dependent on the velocity of the universe relative to the Mach effect thruster. In the SAIC proposal above 5 N/kWe was mooted. This implies a universal velocity of 200 m/s.

Some other implications:

1. The mach effect thruster would be an energy source if the thrust vector is aligned counter to the universal velocity but an energy sink if aligned with it. Have there been any propellant propulsion tests that claim to substantiate this?

2. Mach effect thruster performance would very wildly depending on the time of day or the time of year as the earth's rotates and revolves. Has any propellant propulsion tests noticed this effect?

I will confess up front that this is not a field I follow with any vigor; NASA Spaceflight is about my only source for news in this field. That said, my impression is that the universe is invoked more to evade discussion of conservation laws rather than to explain how they apply. Mach effect propelled ships in particular are analogized often to sailing ships that take momentum and energy from the wind. If there is any thing to the Mach effect the analogy is a good one. I just see little evidence that Mach effect proponents have taken that analogy nearly far enough.

Equation 3 implies that Mach effect thruster performance is heavily dependent on the velocity of the universe relative to the Mach effect thruster. In the SAIC proposal above 5 N/kWe was mooted. This implies a universal velocity of 200 m/s.

Some numbers you should be aware of when trying to figure out the relevant velocities:

Speed due to Earth rotation at Equator: 640 m/sEarth's speed around the sun: 30 km/s (30000 m/s)Speed of sun around center of galaxy: about 200 km/s (200000 m/s)Earth's speed relative to the CMB: about 370 km/s (370000 m/s)

I am not a particular proponent of the Mach effect due to questions related to instantaneous interactions and relativity as well as whether a "velocity of the universe relative to you" can even be defined.

Equation 3 implies that Mach effect thruster performance is heavily dependent on the velocity of the universe relative to the Mach effect thruster. In the SAIC proposal above 5 N/kWe was mooted. This implies a universal velocity of 200 m/s.

Some numbers you should be aware of when trying to figure out the relevant velocities:

Speed due to Earth rotation at Equator: 640 m/sEarth's speed around the sun: 30 km/s (30000 m/s)Speed of sun around center of galaxy: about 200 km/s (200000 m/s)Earth's speed relative to the CMB: about 370 km/s (370000 m/s)

I am not a particular proponent of the Mach effect due to questions related to instantaneous interactions and relativity as well as whether a "velocity of the universe relative to you" can even be defined.

I too, have severe doubts about the instantaneous interactions for Woodward/Mach.

However, I do note that even without the 'instantaneous effect,' gravity is binding over literally interstellar distances - aka stars in the Milky Way are constrained to follow galactic orbits. Given that kind of gravitational strength, it *might* be possible to tap into gravity as a viable source of interstellar travel, maybe even to the point of relativistic velocities.

If the universe gives you a little energy for a MEGA drive, eventually you could get up enough energy to pop a planet or star. We probably do not live in a universe where such self accelerating objects exist.

If the Universe can give you a little energy why can't it give you a lot to warp spacetime? If the device only has KE= energy in but is gaining additional velocity by an effect that cannot be harvested to slam into a stellar object at reletavistic speeds, then once again we do not live in a universe where you can pop planets.

If the universe gives you a little energy for a MEGA drive, eventually you could get up enough energy to pop a planet or star. We probably do not live in a universe where such self accelerating objects exist.

If the Universe can give you a little energy why can't it give you a lot to warp spacetime? If the device only has KE= energy in but is gaining additional velocity by an effect that cannot be harvested to slam into a stellar object at reletavistic speeds, then once again we do not live in a universe where you can pop planets.

Given there are talks about interstellar probes that can go to Proxima in 20 years with believed-to-be feasible improvements of the technology, then yes, we are talking about a technology capable of cracking planets.

Anything that can propel a load at a significant fraction of c can be turned into a weapon just by not braking it and aiming it well.

Please keep in mind the Mach Effect being exploited here is one of triggering a fluctuating mass. what is happening is the electricity being fed to the thruster is changing the active mass from heavy to light. it is a secondary effect born out of the nature of the pzt that rectifies those mass fluctuations into thrust.

From that perspective I do not believe the speed of the universe matters.

I think it is valid to wonder if such a coupling between the device and the gravitational field of the universe is possible. And if so would it allow you to trigger the neccessary mass change in the active mass in the thruster as the device accelerates. Thats the only part that is worth arguing about because if you could magically make a mass heavier and lighter on command while retaining the capability to push when heavy and pull when light you would indeed get thrust, no matter how fast your going while repeating that cycle.

there is a description of the questions and arguments by Jim Davies, in the 4th paragraph.

Very interesting discussion and articles.

Personally and given I'm no physicist, I have some trouble imagining why the intensive use of Mach Effect drives in the locality would result in universal acceleration.

As per the talks elsewhere, the drives would be taking minute amounts of energy and momentum (probably quantum/Planck units of it) from the bodies all across the far reaches of the universe, balancing the energy equations and ensuring entropy always grows.

Nevertheless, for me that means these far bodies would be increasing their entropy as a result, making their orbits slightly more chaotic or losing very small amounts of some other energy (e.g. heat/gravitational potential, etc.) through time in exchange. If we are alone using these drives, the effect on the cosmos may be negligible for a long while. But if there are other civilizations doing it and have been at it for millions of years, I can understand the difference could add up to produce significant cosmic changes.

That means galaxies and bodies losing momentum and crashing into each other, that is, the universe probably losing impulse and contracting. Or is precisely the injection of additional energy in the local region the one somehow causing the acceleration at the expense of the rest?

If it is, I fail to see how. I'd appreciate if anyone with more understanding could elaborate.

If the universe gives you a little energy for a MEGA drive, eventually you could get up enough energy to pop a planet or star. We probably do not live in a universe where such self accelerating objects exist.

If the Universe can give you a little energy why can't it give you a lot to warp spacetime? If the device only has KE= energy in but is gaining additional velocity by an effect that cannot be harvested to slam into a stellar object at reletavistic speeds, then once again we do not live in a universe where you can pop planets.

Given there are talks about interstellar probes that can go to Proxima in 20 years with believed-to-be feasible improvements of the technology, then yes, we are talking about a technology capable of cracking planets.

Anything that can propel a load at a significant fraction of c can be turned into a weapon just by not braking it and aiming it well.

Yeah, well then you've got a very specialized weapon that needs a very long distance to ramp up the velocity to be effective. In that case, even time itself can be a weapon, when everything can be expected to be destroyed in the Heat Death of the Universe.

there is a description of the questions and arguments by Jim Davies, in the 4th paragraph.

Very interesting discussion and articles.

Personally and given I'm no physicist, I have some trouble imagining why the intensive use of Mach Effect drives in the locality would result in universal acceleration.

As per the talks elsewhere, the drives would be taking minute amounts of energy and momentum (probably quantum/Planck units of it) from the bodies all across the far reaches of the universe, balancing the energy equations and ensuring entropy always grows.

Nevertheless, for me that means these far bodies would be increasing their entropy as a result, making their orbits slightly more chaotic or losing very small amounts of some other energy (e.g. heat/gravitational potential, etc.) through time in exchange. If we are alone using these drives, the effect on the cosmos may be negligible for a long while. But if there are other civilizations doing it and have been at it for millions of years, I can understand the difference could add up to produce significant cosmic changes.

That means galaxies and bodies losing momentum and crashing into each other, that is, the universe probably losing impulse and contracting. Or is precisely the injection of additional energy in the local region the one somehow causing the acceleration at the expense of the rest?

If it is, I fail to see how. I'd appreciate if anyone with more understanding could elaborate.

But this is exactly what we are doing in our own solar system by using planets in gravitational assists to sling satellites.

It doesn't matter if the energy is actually free or just effectively free. People would still exploit it. Ultimately it beats all other power sources because they are all limited by their mass. This can pull in energy and mass from somewhere else, forever.

Never underestimate mere human exponential growth. The observable universe is unimaginably vast, but humans, doubling in population every 30 years or so, would crowd it in a mere handful of thousand years, if we were not limited by resource availability.

Suppose we remain limited to light speed, but something like this provides effectively free energy. The maximum sphere of area we could possibly have populated would only expand at a crawl the mere speed of light, but he energy we pull into that sphere would expand exponentially, having dismantled all other available matter for exponential growth, we would also spin this effectively free energy into new matter.

There is a problem here that many would immediately see.. but without FTL, how do you police the entire volume? some groups will choose to keep exponentially expanding and they will dominate.

At some point the linearly increasing volume can not outrun the exponentially increasing density, and human civilisation along with several galaxies vanish, crushed behind an event horizon.

Good insight. And considering the required density of mass for creating an event horizon is not that high if the containing volume is big enough, e.g. I read somewhere a volume the size of the Solar System would collapse into a black hole if it was full of gas as dense as air is in the Everest's top, it's really possible a civilization could entrap itself in a collapsing volume only by being over-enthusiastic using the technology. No need of warring factions using it for nefarious purposes.

I imagine a volume the size of a galaxy would need to be much less dense than air to start the process of gravitational self collapse. Albeit that assumes a really ridiculous amount of use and abuse to cause such an increase of mass-energy inside that volume.

Thus my main objection to this (besides of realism of the phenomenon) is: do we really need to grow exponentially like roaches with an unlimited food supply?

Thus my main objection to this (besides of realism of the phenomenon) is: do we really need to grow exponentially like roaches with an unlimited food supply?

I can't imagine a way, because it only needs a tiny minority, or a self replicating machine, to choose to keep expanding exponentially, and no one could compete with them to stop them.

But who knows. The number of things I cannot imagine is probably infinite.

I suspect also that the event horizon when it formed would not necessarily engulf the entire civilisation, and when it does form it probably puts a severe dent in the exponential growth. The problem would be fully understood by some large proportion of the civilisation so I predict some fraction of the civilisation that devotes all it's effort to speed, and is always ahead of the destruction. Maybe it also keeps leaving boobytraps to slow down the expanding horde behind it, or any other young race that stumbles upon this technology.

It doesn't matter if the energy is actually free or just effectively free. People would still exploit it. Ultimately it beats all other power sources because they are all limited by their mass. This can pull in energy and mass from somewhere else, forever.

Never underestimate mere human exponential growth. The observable universe is unimaginably vast, but humans, doubling in population every 30 years or so, would crowd it in a mere handful of thousand years, if we were not limited by resource availability.

Suppose we remain limited to light speed, but something like this provides effectively free energy. The maximum sphere of area we could possibly have populated would only expand at a crawl the mere speed of light, but he energy we pull into that sphere would expand exponentially, having dismantled all other available matter for exponential growth, we would also spin this effectively free energy into new matter.

There is a problem here that many would immediately see.. but without FTL, how do you police the entire volume? some groups will choose to keep exponentially expanding and they will dominate.

At some point the linearly increasing volume can not outrun the exponentially increasing density, and human civilisation along with several galaxies vanish, crushed behind an event horizon.

If anything, we have seen that humans are tending to breed less and less. Even in some third world countries (like here in Brazil), fertility rates are below 2 children by woman already.

In an advanced interstellar society, I guess couples would wait 100 years before having children...

I am not sure that is accurate measure. Mainly because I think the reason fertility rates are so low in advanced countries is because raising kids is not easy. If the technology this enables drastically reduces the cost both financial and otherwise to raising kids. I can easily see more people having kids on average as a result. Especially if access to that technology is readily available to everyone in the civilization.

Suppose we only double every thousand years. Where are we in a million years of unfettered growth? Have you got a calculator that can handle 21000?

a few ringworlds should suffice.

we shall manage. Even if we have to create dictatorial governments to deal with it.

wars and famines always contributed to cull our population.

War... war never changes. If famine and diseases are things from the past, there will always be new threats... who knows. If it was so easy for a species to multiply until populating the whole universe, then where are them?

It doesn't matter if the energy is actually free or just effectively free. People would still exploit it. Ultimately it beats all other power sources because they are all limited by their mass. This can pull in energy and mass from somewhere else, forever.

Never underestimate mere human exponential growth. The observable universe is unimaginably vast, but humans, doubling in population every 30 years or so, would crowd it in a mere handful of thousand years, if we were not limited by resource availability.

Suppose we remain limited to light speed, but something like this provides effectively free energy. The maximum sphere of area we could possibly have populated would only expand at a crawl the mere speed of light, but he energy we pull into that sphere would expand exponentially, having dismantled all other available matter for exponential growth, we would also spin this effectively free energy into new matter.

There is a problem here that many would immediately see.. but without FTL, how do you police the entire volume? some groups will choose to keep exponentially expanding and they will dominate.

At some point the linearly increasing volume can not outrun the exponentially increasing density, and human civilisation along with several galaxies vanish, crushed behind an event horizon.

If such a technology exists, it could explain Fermi's paradox.

Firstly, energy can also exert gravitation, not just matter. So all you have to do is extract energy from the vacuum - whether you choose to turn it into matter is irrelevant.Nextly, there's that old saying that the only ones who believe in unlimited growth are economists and cancer cells. Recycling mass should be more efficient than extracting it from the vacuum, but even if someone/something were to arise with an endless devotion to extracting energy/mass from the vacuum, then it would eventually succumb to the effects of its own actions (eg. swallowed by the black hole of its own making, as you mentioned)Those who don't want to share in that fate would be forced to find faster ways to escape those who do, or else find ways to eliminate those who do ("fight or flight")